MATH 156 - Calculus I

Instructor: Roberto De Leo.     Term: Fall 2022.     Section 6.

Newton
Cauchy
When & Where: MWTF 2-3pm on Blackboard Collaborate Ultra

Office: Academic Support Building B, Room 214

Office Hours: just email me anytime and we will arrange for a zoom meeting time.

HU Email: roberto DOT deleo AT howard DOT edu

Preferred Email: roberto AT deleo DOT info

Textbook

I will refer in my lectures to the following open source textbook:
M. Boelkins, D. Austin, S. Schlicker, Active Calculus 2.0, CreateSpace Independent Publishing Platform (2018).
The book is available for free in HTML and PDF formats or in paper for about 20$ at Amazon.

Other Textbooks

Studying from a single textbook is seldom a good idea. Below is a list of some other Calculus 1 textbook you might want to consult during the semester:
  1. G. Strang, Calculus VOl. 1, Open Stax
  2. D. Guichard, Calculus - Early Trascendentals, Lyryx
  3. G. Hartman, B. Heinold, T. Siemers, D. Chalishajar, J. Bowen, Apex Calculus, APex
  4. R. Holowinsky, J. Thiel, D. Lindberg, Mooculus Calculus, Mooculus

Videos

Here are a few series of very well done Video Lectures you might use in case you feel the need of hearing more about any of the topics we are going to cover:
  1. Calculus 1 at Grand Valley State University
  2. Calculus 1 full course by T. Basett

Homework

  • Graded Homework will be assigned weekly on Webwork.
  • I will usually provide you a short list of ungraded homework from the suggested textbook. While Webwork problems will usually be straightforward problems, these ungraded ones will be usually harder and are more meant to make you think more about and understand more the topics of the corresponding sections. The list of those problems is in the lectures log below.

    Grades policy

    Grades will be evaluated on the following bases:
    1. Weekly homework: 30%;
    2. Two midterms: 2x25%;
    3. Final exam: 20%.
    Based on the total, you will get the following letter: A (90-100%), B (80-89%), C (70-79%), D (60-69%), F (0-59%).

    Tentative Syllabus

    • Week 1: Continuous functions, Limits.
    • Week 2: Limits, Derivatives.
    • Week 3: Derivatives rules, elementary derivatives.
    • Week 4: Product and quotient rules, chain rule.
    • Week 5: Inverse functions, derivatives of implicit functions.
    • Week 6: Using derivatives to find maxima and minima.
    • Week 7: Global optimization.
    • Week 8: Applied optimization.
    • Week 9: Riemann sums.
    • Week 10: Definite and indefinite integrals.
    • Week 11: Fundamental Theorem of Calculus.
    • Week 12: Integration by substitution.
    • Week 13: Applications of integral and numerical integration.
    • Week 14: Review.

    Collaboration

    Especially with online classes, teamwork is very important and will give you the occasion to interacct with your classmates. You are encouraged in general to work with study partners and also to collaborate on homework. On the other side, you must write your solutions yourself, in your own words, and you must list all collaborators and outside sources of information.
    It is a serious violation of academic integrity to copy an answer without attribution.

    Academic Code of Student Conduct

    (please see Howard University handbook) No copying, unauthorized use of calculators, books, or other materials, or changing of answers or other academic dishonesty will be tolerated. Cheating will not be tolerated. Anyone caught cheating will receive an F for the course and may be expelled from the university.

    Grievance Procedure

    If you have any problems with the policies or rules of this course, discuss your concerns with your instructor. If you are still unable to come to a satisfactory arrangement, you may contact the Director of Undergraduate Studies, Dr. Jill McGowan, and, if still unsatisfied, the Chair of the Department, Dr. Bourama Toni.

    Americans with Disabilities Act

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    The wearing of a face mask as well as compliance with other health protocols while on campus or in the classroom is mandatory. Students will be directed to leave the classroom if a face mask is not worn properly to cover the nose and mouth. Any student who refuses or fails to comply with the University's requirements and precautions against COVID-19, and any other measures the University advances for the safety and protection of the Howard Community, will constitute a violation of the University's Student Code of Conduct and could result in sanctions up to and including expulsion from the University

    Lectures log

    WeekDaySectionsTopicsExercises
    122 AugTo be recovered
    24 AugTo be recovered
    25 AugTo be recovered
    26 AugCourse introduction.
    229 Aug1.1Motivation: average and instantaneous velocity.1.1: 1, 3, 4, 5
    31 Aug1.2The notion of limit.1.2: 1, 3, 4, 5, 6
    1 Sep1.3Derivative at a point.
    2 SepLabour day.
    35 SepLabour day.
    7 Sep1.4The derivative as a function
    8 Sep1.5Using the derivative.
    9 Sep1.5Three different ways to approximate the derivative: Foward Difference, Backward Difference and Central Difference.
    412 Sep1.6Intervals of increase/decrease and up/down concavity: what they are and how to find them. Second Derivative.
    14 Sep1.7Limits and continuity.
    15 Sep1.7Continuity and differentiability.
    16 Sep1.8Local linearization.
    519 Sep1.8, 2.1A last example on the relation between $f$, $f'$ and $f''$. Derivatives of $x^n$ and $a^x$.
    21 Sep2.1Elementary derivative rules
    22 Sep2.3Order of Infinitesimals.
    23 Sep2.4Trig review
    6Sep 262.4Derivative of the tangent function. Vertical and Horizontal asymptotes. Derivatives of cotangent, secant and cosecant functions.
    Sep 282.5Composition of functions. Chain rule.
    Sep 292.5Chain rule.
    Sep 302.6Derivatives of inverse functions.
    7Oct 32.6Derivatives of inverse functions.
    Oct 5Practice testSolving the practice test
    Oct 6Practice testSolving the practice test
    Oct 7Midterm 1
    8Oct 10Mental Health day
    Oct 122.6Derivatives of inverse functions
    Oct 132.7Derivatives of implict functions
    Oct 142.8de L'Hopital's rule
    9Oct 172.8, 3.1Infinitesimals and infinites, Critical points of a function
    Oct 193.1Critical points of a function
    Oct 203.1Activity 3.1.3 and study of $h_k(x)=x^2+\cos(kx)$.
    Oct 213.1, 3.2Study of the families $h_k(x)=x^2+\cos(kx)$ and $p_a(x)=x^3-ax$.
    10Oct 243.2Study of the family $L(t)=\frac{A}{1+ce^{-kt}}$
    Oct 263.3Global Optimization
    Oct 273.4Applied Optimization
    Oct 283.5Related Rates

    Extra Homework #2

    Consider the family of functions $f_a(x)=e^x+\frac{1}{2}ax^2$, where $a$ is a real number and answer the following questions:
    1. Find $f'_a(x)$ and determine the critical numbers for $f_a(x)$.
    2. Construct a first derivative sign chart for $f_a(x)$. What can you say about the overall behavior of $f_a(x)$ if $a>0$? What if $a<0$? In each case, describe the relative extremes of $f_a(x)$.
    3. Find $f''_a(x)$ and construct a second derivative sign chart for $f_a(x)$. What does this tell you about the concavity of $f_a(x)$ if $a>0$? What if $a<0$?
    4. Sketch and label typical graphs of $f_a(x)$ for the cases where $a>0$ and $a<0$. Label all inflection points and local extrema. Use a graphing utility to test your results. Write several sentences to describe your overall conclusions about how the behavior of $f_a(x)$ depends on $f_a(x)$.
    11Oct 31Practice testSolving the practice test.
    Nov 2Review
    Nov 34.1Finding the distance covered $\Delta s$ from the velocity function $v(t)$.
    Nov 44.1Going over activities in 4.1
    12Nov 7Midterm 2
    Nov 94.2Riemann sums
    Nov 104.2Riemann sums
    Nov 11Veteran's day
    13Nov 144.3The Definite Integral
    Nov 164.4The Fundamental Theorem of Calculus
    Nov 175.1Graph of the antiderivative
    Nov 185.1Graph of the antiderivative
    14Nov 215.2The second fundamental theorem of calculus
    Nov 235.3Integration by substitution
    Nov 24Thanksgiving
    Nov 25Thanksgiving
    15Nov 28NotesReview
    Nov 30Midterm 3
    Dec 16.1Using Definite Integrals to Find Area and Length
    Dec 26.2, 6.3Volume, Density, Mass, and Center of Mass
    Dec 3NotesReview: solving Spring 2022 Calc 1 final
    Dec 4